Characterizations of the adjugate map

dc.contributor.advisorSinkhorn, Richard D.
dc.contributor.committeeMemberHardy, John T.
dc.contributor.committeeMemberByrd, Richard D.
dc.contributor.committeeMemberWood, Lowell T.
dc.creatorSever, Timor
dc.description.abstractIn this thesis, we discuss properties and characterizations of the adjugate map; that is the function that assigns to a complex matrix A the matrix consisting of the cofactors of A. The characterizations we develop arise from basic properties of the adjugate map. One important property of the adjugate function is that it is anti-product preserving. We present certain sets of abstract conditions and we show that these conditions define the adjugate function. Each nonsingular matrix Z can be expressed as a finite product of elementary matrices. Hence, using the anti-commutativity of the adjugate map we can express the image of an arbitrary nonsingular matrix in terms of the images of elementary matrices. We use this fact to verify whether the sets of conditions considered define the adjugate function. We attempt to minimize the number of conditions necessary to characterize the adjugate map.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginreformatted digital
dc.relation.ispartofSenior Honors Theses
dc.rightsThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.
dc.titleCharacterizations of the adjugate map
dc.type.genreThesis of Natural Sciences and Mathematics, Department of of Houston of Science


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